1 Catastrophe Insurance Products in Markov Jump Diffusion Model

For catastrophic events, the assumption that catastrophe claims occur in terms of the Poisson process is inadequate as it has constant intensity. This article proposes Markov Modulated Poisson process (MMPP) to model the arrival process for catastrophic events. Under this process, the underlying state is governed by a homogenous Markov chain, and it is the generalization of Cummins and Geman (1993), Chang, Chang, and Yu (1996) and Geman and Yor (1997). We apply Markov jump diffusion model to derive pricing formulas and hedging formulas for catastrophe insurance products, included futures call option, catastrophe PCS call spread and catastrophe bond. The numerical analysis shows how the catastrophe insurance products prices are related to jump rate of catastrophe events, standard deviation of jump size, and mean of jump size